Elements of geometry and trigonometry . n two angles and the included side of theone are equal to two angles and the included side of the other,each to each. For, one of these triangles, or the triangle symmetrical WMthit, may be placed on tlie other, as is done in the corres-ponding case of rectilineal triangles (Book I. Prop. VI.). PROPOSITION XII. THEOREM. If two tiiangles on the same sphere, or on equal spheres, have alltheir sides equal, each to each, their angles will likewise beequal, each to each, the equal angles lying opposite the equalsides. 190 GEOMETRY. This truth is evident from
Elements of geometry and trigonometry . n two angles and the included side of theone are equal to two angles and the included side of the other,each to each. For, one of these triangles, or the triangle symmetrical WMthit, may be placed on tlie other, as is done in the corres-ponding case of rectilineal triangles (Book I. Prop. VI.). PROPOSITION XII. THEOREM. If two tiiangles on the same sphere, or on equal spheres, have alltheir sides equal, each to each, their angles will likewise beequal, each to each, the equal angles lying opposite the equalsides. 190 GEOMETRY. This truth is evident from Prop. IX,where it was shown, that with three givensides AB, AC, BC, there can only be twotriangles ACB, ABD, differing as to theposition of their parts, and equal as to themagnitude of those parts. Hence thosetwo triangles, having all their sides re-spectively equal in both, must either beabsolutely equal, or at least symmetricallyso ; in either of which cases, their corres-ponding angles must be equal, and lie opposite to equal
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